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Calculate the total cost for two different delivery options for 1200 boxes. Option A charges R18.50 per box. Option B charges R10,000 for up to 800 boxes and R25 for each additional box.

Business/Management

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Answers

4 parts
a

R22200\text{R}22200

b

R20000\text{R}20000

c

Option B\text{Option B}

d

Option B\text{Option B}

Step-by-step solution

11 steps

Here are the calculations for the delivery options.

Part a· 2 steps

Calculate the total cost of using Option A to transport all 1200 boxes.

  1. Identify the cost per box for Option A.

    Option A charges R18.50 per box.

  2. Calculate the total cost for 1200 boxes.

    CostOption A=Number of boxes×Cost per box\text{Cost}_{\text{Option A}} = \text{Number of boxes} \times \text{Cost per box} CostOption A=1200×R18.50\text{Cost}_{\text{Option A}} = 1200 \times \text{R}18.50 CostOption A=R22200\text{Cost}_{\text{Option A}} = \text{R}22200

    The total cost for Option A is R22200\boxed{\text{R}22200}.

Part b

R20000\text{R}20000

Calculate the total cost of using Option B.

  1. Identify the flat rate and additional box charge for Option B.

    Option B charges a flat rate of R10 000 for up to 800 boxes.
    Any additional box is charged at R25 per box.

  2. Calculate the number of additional boxes.

    Total boxes = 1200.
    Boxes covered by flat rate = 800.
    Additional boxes = 1200−800=4001200 - 800 = 400 boxes.

  3. Calculate the cost for the additional boxes.

    Costadditional=Number of additional boxes×Cost per additional box\text{Cost}_{\text{additional}} = \text{Number of additional boxes} \times \text{Cost per additional box} Costadditional=400×R25\text{Cost}_{\text{additional}} = 400 \times \text{R}25 Costadditional=R10000\text{Cost}_{\text{additional}} = \text{R}10000

  4. Calculate the total cost for Option B.

    CostOption B=Flat rate+Costadditional\text{Cost}_{\text{Option B}} = \text{Flat rate} + \text{Cost}_{\text{additional}} CostOption B=R10000+R10000\text{Cost}_{\text{Option B}} = \text{R}10000 + \text{R}10000 CostOption B=R20000\text{Cost}_{\text{Option B}} = \text{R}20000

    The total cost for Option B is R20000\boxed{\text{R}20000}.

Part c

Option B\text{Option B}

Based on cost alone, which option is more affordable?

  1. Compare the total costs of Option A and Option B.

    Cost of Option A = R22 200.
    Cost of Option B = R20 000.

  2. Determine the more affordable option.

    Since R20 000 < R22 200, Option B is more affordable.
    Based on cost alone, Option B\boxed{\text{Option B}} is more affordable.

Part d

Option B\text{Option B}

If the company values faster delivery and is willing to pay up to R2 500 extra for same-day delivery, which option should they choose? Justify your answer.

  1. Determine the difference in cost between Option A and Option B.

    Cost difference=CostOption A−CostOption B\text{Cost difference} = \text{Cost}_{\text{Option A}} - \text{Cost}_{\text{Option B}} Cost difference=R22200−R20000\text{Cost difference} = \text{R}22200 - \text{R}20000 Cost difference=R2200\text{Cost difference} = \text{R}2200

    Option B is R2200 cheaper than Option A.

  2. Consider the delivery times and the company's willingness to pay for faster delivery.

    Option A delivers in 2 days. Option B delivers in 1 day (faster delivery).
    The company is willing to pay up to R2 500 extra for same-day delivery (which Option B provides).

  3. Compare the cost difference with the acceptable extra payment.

    The actual cost difference is R2200 (Option B is cheaper by this amount).
    Since Option B is R2200 cheaper and provides faster delivery (1 day vs 2 days), it is within the company's willingness to pay up to R2500 extra for faster delivery. In fact, they save money while getting faster delivery.
    The company should choose Option B\boxed{\text{Option B}}. This is because Option B delivers in 1 day, which is faster than Option A's 2 days, and it is also R2200 cheaper. This saving is well within the R2500 extra the company is willing to pay for faster delivery.

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